Jun 16 07:00 AM PDT  09:00 AM PDT Get personalized insights and an accurate assessment of your current quant score to achieve your Target Quant Score. Jun 16 09:00 PM PDT  10:00 PM PDT For a score of 4951 (from current actual score of 40+). AllInOne Standard & 700+ Level Questions (150 questions) Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease.
Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 06 Jul 2014
Posts: 1229
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
Updated on: 07 Apr 2015, 04:40
Question Stats:
23% (01:31) correct 77% (01:24) wrong based on 194 sessions
HideShow timer Statistics
Is \((x+y)(xy) =\) even integer? 1) \(x^2+y^2 =\) even 2) \(x+y =\)even Source: selfmade
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Originally posted by Harley1980 on 06 Apr 2015, 11:19.
Last edited by Harley1980 on 07 Apr 2015, 04:40, edited 3 times in total.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9320
Location: Pune, India

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
07 Apr 2015, 02:08
Harley1980 wrote: Is \((x+y)(xy) =\) even integer?
1) \(x^2+y^2 =\) even
2) \(x+y =\)even So now the question is  what is the actual answer? Try using both statements together: If you know that \(x + y\) is an even integer and \(x^2 + y^2\) is an even integer, is it necessary that \(x^2  y^2\) should be an even integer too? Actually, no! It is easy to show that if x and y are both even/both odd integers, then \(x+y\) is even, \(x^2 + y^2\) is even and \(x^2  y^2\) is even. But how do you figure out a case where \(x+y\) is even, \(x^2 + y^2\) is even but \(x^2  y^2\) is not an even integer? Let me give you an example: Say \(x = 3+\sqrt{6}\) and \(y = 3  \sqrt{6}\). Here, \(x + y = 6\) (even integer) \(x^2 + y^2 = 30\) (even integer) But \(x^2  y^2 = 12\sqrt{6}\) So answer is (E). What you should think about is: How can you prove with variables that answer is (E)? Perhaps, the form of x and y that I have given as an example can help you!
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Current Student
Joined: 13 Nov 2014
Posts: 108

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
06 Apr 2015, 14:22
Am i missing something simple? A)(x+y)(xy) = x^2+y^2 and we are told that is even... so suff B) we are told (x+y) is even. even * even = even and odd * even = even . Even if (xy) = 0, gmat considers 0 as even. So Suff
_________________
Gmat prep 1 600 Veritas 1 650 Veritas 2 680 Gmat prep 2 690 (48Q 37V) Gmat prep 5 730 (47Q 42V) Gmat prep 6 720 (48Q 41V)



Retired Moderator
Joined: 06 Jul 2014
Posts: 1229
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
06 Apr 2015, 14:30
Wofford09 wrote: Am i missing something simple?
A)(x+y)(xy) = x^2+y^2 and we are told that is even... so suff
B) we are told (x+y) is even. even * even = even and odd * even = even . Even if (xy) = 0, gmat considers 0 as even. So Suff about A) \((x+y)(xy)\) not equal to \(x^2+y^2\) it is equal to \(x^2y^2\) about B) Let's assume that \(x =\frac{5}{3}\) and \(y = \frac{1}{3}\), \(x + y = \frac{5}{3}+\frac{1}{3} = \frac{6}{3} = 2\) but \(x^2+y^2\) will be equal to \((\frac{5}{3})^2 + (\frac{1}{3})^2 = \frac{25}{9}+\frac{1}{9} =\frac{26}{9}\) not even
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9320
Location: Pune, India

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
06 Apr 2015, 20:50
Harley1980 wrote: Wofford09 wrote: Am i missing something simple?
A)(x+y)(xy) = x^2+y^2 and we are told that is even... so suff
B) we are told (x+y) is even. even * even = even and odd * even = even . Even if (xy) = 0, gmat considers 0 as even. So Suff about A) \((x+y)(xy)\) not equal to \(x^2+y^2\) it is equal to \(x^2y^2\) about B) Let's assume that \(x =\frac{5}{3}\) and \(y = \frac{1}{3}\), \(x + y = \frac{5}{3}+\frac{1}{3} = \frac{6}{3} = 2\) but \(x^2+y^2\) will be equal to \((\frac{5}{3})^2 + (\frac{1}{3})^2 = \frac{25}{9}+\frac{1}{9} =\frac{26}{9}\) not even Using the same logic, think what happens in stmnt 1 when \(x^2 = 5/3\) and \(y^2 = 1/3\). In this case, \(x^2 + y^2 = 2\) (even) but \(x^2  y^2 = 4/3\) (not an even integer) but if \(x^2 = 12\) and \(y^2 = 6\), both \(x^2 + y^2\) and \(x^2  y^2\) are even. So how can the answer be (A)?
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Retired Moderator
Joined: 06 Jul 2014
Posts: 1229
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
06 Apr 2015, 23:15
VeritasPrepKarishma wrote: Harley1980 wrote: Wofford09 wrote: Am i missing something simple?
A)(x+y)(xy) = x^2+y^2 and we are told that is even... so suff
B) we are told (x+y) is even. even * even = even and odd * even = even . Even if (xy) = 0, gmat considers 0 as even. So Suff about A) \((x+y)(xy)\) not equal to \(x^2+y^2\) it is equal to \(x^2y^2\) about B) Let's assume that \(x =\frac{5}{3}\) and \(y = \frac{1}{3}\), \(x + y = \frac{5}{3}+\frac{1}{3} = \frac{6}{3} = 2\) but \(x^2+y^2\) will be equal to \((\frac{5}{3})^2 + (\frac{1}{3})^2 = \frac{25}{9}+\frac{1}{9} =\frac{26}{9}\) not even Using the same logic, think what happens in stmnt 1 when \(x^2 = 5/3\) and \(y^2 = 1/3\). In this case, \(x^2 + y^2 = 2\) (even) but \(x^2  y^2 = 4/3\) (not an even integer) but if \(x^2 = 12\) and \(y^2 = 6\), both \(x^2 + y^2\) and \(x^2  y^2\) are even. So how can the answer be (A)? Wow, that's amazing. VeritasPrepKarishma, you have an eagle eye ) Thank you.
_________________



Manager
Joined: 17 Mar 2015
Posts: 116

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
Updated on: 07 Apr 2015, 00:22
My solution: For the first option: \(X^2 + Y^2 =\) even, then if you add or subtract \(2*X*Y\), you will get an even number aswell, so \(X^2 + Y^2 + 2*X*Y = (X + Y)^2\) is even and \((X  Y)^2\) is even too. Say both of them are \(2*k\) and \(2*b\) respectively. \(\sqrt{2*k}*\sqrt{2*b} = 2*\sqrt{k}*\sqrt{b}\) which is even, thus #1 is sufficient. For the second  well, its quite obvious: product of even number with whatever = even, thats true, thus sufficient
C it is then edit: meant D, which is, sadly, incorrect.
Originally posted by Zhenek on 07 Apr 2015, 00:11.
Last edited by Zhenek on 07 Apr 2015, 00:22, edited 1 time in total.



Retired Moderator
Joined: 06 Jul 2014
Posts: 1229
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
07 Apr 2015, 00:15
Zhenek wrote: My solution: For the first option: \(X^2 + Y^2 =\) even, then if you add or subtract \(2*X*Y\), you will get an even number aswell, so \(X^2 + Y^2 + 2*X*Y = (X + Y)^2\) is even and \((X  Y)^2\) is even too. Say both of them are \(2*k\) and \(2*b\) respectively. \(\sqrt{2*k}*\sqrt{2*b} = 2*\sqrt{k}*\sqrt{b}\) which is even, thus #1 is sufficient. For the second  well, its quite obvious: product of even number with whatever = even, thats true, thus sufficient
C it is then Zhenek, this is look as you say that answer D is right: both statements are sufficient by themselves. Am I right?
_________________



Manager
Joined: 17 Mar 2015
Posts: 116

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
Updated on: 07 Apr 2015, 02:35
Harley1980 wrote: Zhenek wrote: My solution: For the first option: \(X^2 + Y^2 =\) even, then if you add or subtract \(2*X*Y\), you will get an even number aswell, so \(X^2 + Y^2 + 2*X*Y = (X + Y)^2\) is even and \((X  Y)^2\) is even too. Say both of them are \(2*k\) and \(2*b\) respectively. \(\sqrt{2*k}*\sqrt{2*b} = 2*\sqrt{k}*\sqrt{b}\) which is even, thus #1 is sufficient. For the second  well, its quite obvious: product of even number with whatever = even, thats true, thus sufficient
C it is then Zhenek, this is look as you say that answer D is right: both statements are sufficient by themselves. Am I right? Oh, yea, I guess I meant that indeed, not experienced with the gmat thing yet. Looks like my answer is wrong then, what a bummer. I guess I really need to pay attention to the given info (no information given about X and Y being nonintegers, which completely blows my solution from the getgo: \(2*X*Y\) could be \(2*\sqrt{5}/2*\sqrt{3}/2\) which is not even remotely even )
Originally posted by Zhenek on 07 Apr 2015, 00:18.
Last edited by Zhenek on 07 Apr 2015, 02:35, edited 2 times in total.



Manager
Joined: 17 Mar 2015
Posts: 116

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
07 Apr 2015, 02:38
Well then, lets amend my approach. Lets start from getgo.
Looking at 1st option and taking into account the fact that X and Y could be nonintegers, we can't really say anything about the answer to the question with just option 1 on its own, I'd just call it insufficient right away after comming up with 2 different examples, one being integer and another  noninteger. Easiest ones that come into mind are: 1)X = 1, Y = 1: 2 is even, 0 is even 2)X = \(\sqrt{5}/2\), Y = \(\sqrt{3}/2\): 2 is even, 1/2 is not even This makes #1 insufficient on its own.
#2  same story, take fractions as second example and integers as first example, insufficient on its own.
Now lets look at them together \(x^2 + y^2 = 2*k\) \(x + y = 2*m\) => \(y = 2*m  x\) \(x^2 + y^2 = (x+y)^2  2*x*y = (x+y)^2  2*x*(2*mx) = 4*m^2 2*x*(2*m  x) = 2*k\) \(2*k = 4*m^2  2*x*(2*m  x)\) => \(x^2 2*m*x + 2*m^2  k = 0\) \(x = m\)±\(\sqrt{k  m^2}\) \(y = 2*m  x = m\)∓\(\sqrt{k  m^2}\) So we found values of X and Y that would match 2 of these equation(both #1 and #2). That being said, k and m are random positive integers thus we can't be sure if the expression under the root is a perfect square or not. If you input these values into your question, you will get \(x^2  y^2 = (xy)*(x+y) =\)±\(4*m*\sqrt{k  m^2}\) which unfortunatelly doesn't answer our question coz of root's value being uncertain (perfect square, then answer is "even", if it is not perfect square, then answer is "not even") The answer E, yet again, contradicts the OA, which is unfortunate.



Retired Moderator
Joined: 06 Jul 2014
Posts: 1229
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
07 Apr 2015, 04:43
Looks like my first attempt to make a task became a train wreck VeritasPrepKarishma, Zhenek thanks for your explanations, it is now clear. I've changed answer to E. Looks like this isn't 600700 lvl task.
_________________



Manager
Joined: 21 Oct 2017
Posts: 80
Location: France
Concentration: Entrepreneurship, Technology
GPA: 4
WE: Project Management (Internet and New Media)

Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
28 Nov 2017, 12:04
I had a hard time with this question. I would like to better understand what went wrong in my approach: The question is: \((X + Y)(X  Y)\) = Even? Which I rephrased too: \(X^2 + Y^2  2XY\) = Even? Hence, when looking at statement 1 and 2, I'm able to asses that X and Y need to either both be Even or Odd, and \(2XY\) has to be Even. So I just went on to select D. Please help me understand why I can't take this shortcut and I fell right into it. Thanks,
_________________
Please Press +1 Kudos if it helps!
October 9th, 2017: Diagnostic Exam  Admit Master (GoGMAT)  640 November 11th, 2017: CAT 1  Admit Master (GoGMAT)  700 November 20th, 2017: CAT 2  GMATPrep  700 (Q: 47, V: 40) November 25th, 2017: CAT 3  Admit Master (GoGMAT)  710 (Q: 48, V: 40) November 27th, 2017: CAT 4  GMATPrep  720 (Q: 49, V: 40)
December 4th, 2017: GMAT Exam  750 (Q: 48, V: 44, IR: 8, AWA: 6)



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9320
Location: Pune, India

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
29 Nov 2017, 03:38
Hadrienlbb wrote: I had a hard time with this question. I would like to better understand what went wrong in my approach: The question is: \((X + Y)(X  Y)\) = Even? Which I rephrased too: \(X^2 + Y^2  2XY\) = Even? Hence, when looking at statement 1 and 2, I'm able to asses that X and Y need to either both be Even or Odd, and \(2XY\) has to be Even. So I just went on to select D. Please help me understand why I can't take this shortcut and I fell right into it. Thanks, Note that \((X + Y)*(X  Y) = X^2  Y^2\)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 21 Oct 2017
Posts: 80
Location: France
Concentration: Entrepreneurship, Technology
GPA: 4
WE: Project Management (Internet and New Media)

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
30 Nov 2017, 18:06
OMG I swear I have not been drinking. Just working too hard! Nonetheless, this is unacceptable of me. Thanks very much Karishma, and forgive my carelessness. VeritasPrepKarishma wrote: Hadrienlbb wrote: I had a hard time with this question. I would like to better understand what went wrong in my approach: The question is: \((X + Y)(X  Y)\) = Even? Which I rephrased too: \(X^2 + Y^2  2XY\) = Even? Hence, when looking at statement 1 and 2, I'm able to asses that X and Y need to either both be Even or Odd, and \(2XY\) has to be Even. So I just went on to select D. Please help me understand why I can't take this shortcut and I fell right into it. Thanks, Note that \((X + Y)*(X  Y) = X^2  Y^2\)
_________________
Please Press +1 Kudos if it helps!
October 9th, 2017: Diagnostic Exam  Admit Master (GoGMAT)  640 November 11th, 2017: CAT 1  Admit Master (GoGMAT)  700 November 20th, 2017: CAT 2  GMATPrep  700 (Q: 47, V: 40) November 25th, 2017: CAT 3  Admit Master (GoGMAT)  710 (Q: 48, V: 40) November 27th, 2017: CAT 4  GMATPrep  720 (Q: 49, V: 40)
December 4th, 2017: GMAT Exam  750 (Q: 48, V: 44, IR: 8, AWA: 6)



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9320
Location: Pune, India

Re: Is (x+y)(xy) = even integer?
[#permalink]
Show Tags
01 Dec 2017, 00:30
Hadrienlbb wrote: OMG I swear I have not been drinking. Just working too hard! Nonetheless, this is unacceptable of me. Thanks very much Karishma, and forgive my carelessness. VeritasPrepKarishma wrote: Hadrienlbb wrote: I had a hard time with this question. I would like to better understand what went wrong in my approach: The question is: \((X + Y)(X  Y)\) = Even? Which I rephrased too: \(X^2 + Y^2  2XY\) = Even? Hence, when looking at statement 1 and 2, I'm able to asses that X and Y need to either both be Even or Odd, and \(2XY\) has to be Even. So I just went on to select D. Please help me understand why I can't take this shortcut and I fell right into it. Thanks, Note that \((X + Y)*(X  Y) = X^2  Y^2\) It is better to make these errors during practice so that you do not make them during the actual exam!!
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Re: Is (x+y)(xy) = even integer?
[#permalink]
01 Dec 2017, 00:30






